Subgroups — C₃₁×#34449 #21491208

Order 7936.

2074 conjugacy classes of subgroups.

The subgroup lattice has 1428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#539	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2382	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2378	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2378	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2376	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2374	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2373	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2373	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2371	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2370	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2370	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2362	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#2360	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2357	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2352	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2345	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2344	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#2335	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2335	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#2335	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2335	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2334	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2334	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#2333	C₂	1	1	yes	maximal, characteristic
25	C₃₁×#2332	C₂	1	1	yes	maximal, characteristic, complemented
26	C₃₁×#2324	C₂	1	1	yes	maximal, characteristic
27	C₃₁×#2322	C₂	1	1	yes	maximal, characteristic, complemented
28	C₃₁×#2319	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×C₃₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×C₃₁×#123	C₂	1	1	yes	maximal, characteristic, complemented
31	C₃₁×#2290	C₂	1	1	yes	maximal, characteristic, complemented
32	C₃₁×#539	C₄	1	16	yes	complemented
33	C₂×C₃₁×#126	C₂²	1	1	yes	characteristic
34	C₂×C₃₁×#126	C₂²	1	1	yes	characteristic
35	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
36	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
37	C₂×C₃₁×#123	C₂²	1	1	yes	characteristic
38	C₂×C₃₁×#123	C₂²	1	1	yes	characteristic
39	C₂×C₃₁×#123	C₂²	1	1	yes	characteristic
40	C₂×C₃₁×#123	C₂²	1	1	yes	characteristic
41	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
43	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
44	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
49	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
50	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
51	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
52	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
53	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
54	C₃₁×#391	C₂²	1	1	yes	characteristic
55	C₃₁×#391	C₂²	1	1	yes	characteristic
56	C₃₁×#391	C₂²	1	1	yes	characteristic
57	C₃₁×#390	C₂²	1	1	yes	characteristic
58	C₃₁×#390	C₂²	1	1	yes	characteristic
59	C₃₁×#390	C₂²	1	1	yes	characteristic
60	C₃₁×#390	C₂²	1	1	yes	characteristic
61	C₃₁×#390	C₂²	1	1	yes	characteristic
62	C₃₁×#389	C₂²	1	1	yes	characteristic
63	C₃₁×#389	C₂²	1	1	yes	characteristic
64	C₃₁×#389	C₂²	1	1	yes	characteristic
65	C₃₁×#389	C₂²	1	1	yes	characteristic
66	C₃₁×#389	C₂²	1	1	yes	characteristic
67	C₃₁×#389	C₂²	1	1	yes	characteristic
68	C₃₁×#389	C₂²	1	1	yes	characteristic
69	C₃₁×#389	C₂²	1	1	yes	characteristic
70	C₃₁×#389	C₂²	1	1	yes	characteristic
71	C₃₁×#389	C₂²	1	1	yes	characteristic
72	C₃₁×#389	C₂²	1	1	yes	characteristic
73	C₃₁×#389	C₂²	1	1	yes	characteristic
74	C₃₁×#389	C₂²	1	1	yes	characteristic
75	C₃₁×#389	C₂²	1	1	yes	characteristic
76	C₃₁×#388	C₂²	1	1	yes	characteristic
77	C₃₁×#388	C₂²	1	1	yes	characteristic
78	C₃₁×#388	C₂²	1	1	yes	characteristic
79	C₃₁×#388	C₂²	1	1	yes	characteristic
80	C₃₁×#388	C₂²	1	1	yes	characteristic
81	C₃₁×#388	C₂²	1	1	yes	characteristic
82	C₃₁×#388	C₂²	1	1	yes	characteristic
83	C₃₁×#388	C₂²	1	1	yes	characteristic
84	C₃₁×#388	C₂²	1	1	yes	characteristic
85	C₃₁×#388	C₂²	1	1	yes	characteristic
86	C₃₁×#388	C₂²	1	1	yes	characteristic
87	C₃₁×#388	C₂²	1	1	yes	characteristic
88	C₃₁×#388	C₂²	1	1	yes	characteristic
89	C₃₁×#388	C₂²	1	1	yes	characteristic
90	C₃₁×#388	C₂²	1	1	yes	characteristic
91	C₃₁×#388	C₂²	1	1	yes	characteristic
92	C₃₁×#388	C₂²	1	1	yes	characteristic
93	C₃₁×#388	C₂²	1	1	yes	characteristic
94	C₃₁×#388	C₂²	1	1	yes	characteristic
95	C₃₁×#388	C₂²	1	1	yes	characteristic
96	C₃₁×#388	C₂²	1	1	yes	characteristic
97	C₃₁×#388	C₂²	1	1	yes	characteristic
98	C₃₁×#388	C₂²	1	1	yes	characteristic
99	C₃₁×#388	C₂²	1	1	yes	characteristic
100	C₃₁×#387	C₂²	1	1	yes	characteristic
101	C₃₁×#387	C₂²	1	1	yes	characteristic
102	C₃₁×#387	C₂²	1	1	yes	characteristic
103	C₃₁×#387	C₂²	1	1	yes	characteristic
104	C₃₁×#387	C₂²	1	1	yes	characteristic
105	C₃₁×#387	C₂²	1	1	yes	characteristic
106	C₃₁×#387	C₂²	1	1	yes	characteristic
107	C₃₁×#387	C₂²	1	1	yes	characteristic
108	C₃₁×#387	C₂²	1	1	yes	characteristic
109	C₃₁×#387	C₂²	1	1	yes	characteristic
110	C₃₁×#387	C₂²	1	1	yes	characteristic
111	C₃₁×#387	C₂²	1	1	yes	characteristic
112	C₃₁×#387	C₂²	1	1	yes	characteristic
113	C₃₁×#387	C₂²	1	1	yes	characteristic
114	C₃₁×#387	C₂²	1	1	yes	characteristic
115	C₃₁×#387	C₂²	1	1	yes	characteristic
116	C₃₁×#387	C₂²	1	1	yes	characteristic
117	C₃₁×#387	C₂²	1	1	yes	characteristic
118	C₃₁×#387	C₂²	1	1	yes	characteristic
119	C₃₁×#387	C₂²	1	1	yes	characteristic
120	C₃₁×#387	C₂²	1	1	yes	characteristic
121	C₃₁×#387	C₂²	1	1	yes	characteristic
122	C₃₁×#387	C₂²	1	1	yes	characteristic
123	C₃₁×#387	C₂²	1	1	yes	characteristic
124	C₃₁×#387	C₂²	1	1	yes	characteristic
125	C₃₁×#387	C₂²	1	1	yes	characteristic
126	C₃₁×#387	C₂²	1	1	yes	characteristic
127	C₃₁×#387	C₂²	1	1	yes	characteristic
128	C₃₁×#386	C₂²	1	1	yes	characteristic
129	C₃₁×#386	C₂²	1	1	yes	characteristic
130	C₃₁×#386	C₂²	1	1	yes	characteristic
131	C₃₁×#386	C₂²	1	1	yes	characteristic
132	C₃₁×#386	C₂²	1	1	yes	characteristic
133	C₃₁×#386	C₂²	1	1	yes	characteristic
134	C₃₁×#385	C₂²	1	1	yes	characteristic
135	C₃₁×#385	C₂²	1	1	yes	characteristic
136	C₃₁×#385	C₂²	1	1	yes	characteristic
137	C₃₁×#385	C₂²	1	1	yes	characteristic
138	C₃₁×#385	C₂²	1	1	yes	characteristic
139	C₃₁×#385	C₂²	1	1	yes	characteristic
140	C₃₁×#385	C₂²	1	1	yes	characteristic
141	C₃₁×#385	C₂²	1	1	yes	characteristic
142	C₃₁×#382	C₂²	1	1	yes	characteristic
143	C₃₁×#382	C₂²	1	1	yes	characteristic
144	C₃₁×#381	C₂²	1	1	yes	characteristic
145	C₃₁×#381	C₂²	1	1	yes	characteristic
146	C₃₁×#381	C₂²	1	1	yes	characteristic
147	C₃₁×#381	C₂²	1	1	yes	characteristic
148	C₃₁×#380	C₂²	1	1	yes	characteristic
149	C₃₁×#380	C₂²	1	1	yes	characteristic
150	C₃₁×#380	C₂²	1	1	yes	characteristic
151	C₃₁×#380	C₂²	1	1	yes	characteristic
152	C₃₁×#380	C₂²	1	1	yes	characteristic
153	C₃₁×#380	C₂²	1	1	yes	characteristic
154	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
155	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
156	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
157	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
158	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
159	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
160	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
161	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
162	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
163	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
164	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
165	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
166	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
167	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
168	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
169	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
170	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
171	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
172	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
173	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
174	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
175	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
176	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
177	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
178	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
179	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
180	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
181	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
182	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
183	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
184	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
185	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
186	C₃₁×#376	C₂²	1	1	yes	characteristic
187	C₃₁×#376	C₂²	1	1	yes	characteristic
188	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
189	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
190	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
191	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
192	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
193	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
194	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
195	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
196	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
197	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
198	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
199	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
200	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
201	C₃₁×#126	C₂×C₄	1	8	yes	complemented
202	C₃₁×#126	C₂×C₄	1	8	yes	complemented
203	C₃₁×#125	C₂×C₄	1	8	yes	complemented
204	C₃₁×#125	C₂×C₄	1	8	yes	complemented
205	C₃₁×#123	C₂×C₄	1	8	yes	—
206	C₃₁×#123	C₂×C₄	1	8	yes	—
207	C₃₁×#123	C₂×C₄	1	8	yes	complemented
208	C₃₁×#123	C₂×C₄	1	8	yes	complemented
209	C₃₁×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
210	C₃₁×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
211	C₃₁×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
212	C₃₁×#121	C₂×C₄	1	8	yes	—
213	C₄×Q₈×C₃₁	—	4	2	no	—
214	C₄×D₄×C₃₁	—	4	2	no	—
215	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
216	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
217	C₃₁×#117	—	4	2	no	—
218	C₃₁×#117	—	4	2	no	—
219	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
220	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	8	yes	complemented
221	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
240	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
241	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
242	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
260	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
268	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
270	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
272	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
273	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
280	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
281	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
285	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
286	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
287	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
288	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
289	C₂×C₄²×C₃₁	—	4	2	no	—
290	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
291	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
292	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
293	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
294	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
295	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
296	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
297	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
298	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
300	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
301	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
302	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
303	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
304	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
305	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
306	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
307	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
308	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
309	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
310	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
311	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
312	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
313	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
314	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
315	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
316	C₃₁×#95	C₂³	1	1	yes	characteristic
317	C₃₁×#95	C₂³	1	1	yes	characteristic
318	C₃₁×#95	C₂³	1	1	yes	characteristic
319	C₃₁×#95	C₂³	1	1	yes	characteristic
320	C₃₁×#95	C₂³	1	1	yes	characteristic
321	C₃₁×#95	C₂³	1	1	yes	characteristic
322	C₃₁×#95	C₂³	1	1	yes	characteristic
323	C₃₁×#95	C₂³	1	1	yes	characteristic
324	C₃₁×#95	C₂³	1	1	yes	characteristic
325	C₃₁×#95	C₂³	1	1	yes	characteristic
326	C₃₁×#95	C₂³	1	1	yes	characteristic
327	C₃₁×#95	C₂³	1	1	yes	characteristic
328	C₃₁×#95	C₂³	1	1	yes	characteristic
329	C₃₁×#95	C₂³	1	1	yes	characteristic
330	C₃₁×#95	C₂³	1	1	yes	characteristic
331	C₃₁×#95	C₂³	1	1	yes	characteristic
332	C₃₁×#95	C₂³	1	1	yes	characteristic
333	C₃₁×#95	C₂³	1	1	yes	characteristic
334	C₃₁×#95	C₂³	1	1	yes	characteristic
335	C₃₁×#95	C₂³	1	1	yes	characteristic
336	C₃₁×#95	C₂³	1	1	yes	characteristic
337	C₃₁×#95	C₂³	1	1	yes	characteristic
338	C₃₁×#95	C₂³	1	1	yes	characteristic
339	C₃₁×#95	C₂³	1	1	yes	characteristic
340	C₃₁×#95	C₂³	1	1	yes	characteristic
341	C₃₁×#95	C₂³	1	1	yes	characteristic
342	C₃₁×#95	C₂³	1	1	yes	characteristic
343	C₃₁×#95	C₂³	1	1	yes	characteristic
344	C₃₁×#95	C₂³	1	1	yes	characteristic
345	C₃₁×#95	C₂³	1	1	yes	characteristic
346	C₃₁×#95	C₂³	1	1	yes	characteristic
347	C₃₁×#95	C₂³	1	1	yes	characteristic
348	C₃₁×#95	C₂³	1	1	yes	characteristic
349	C₃₁×#95	C₂³	1	1	yes	characteristic
350	C₃₁×#95	C₂³	1	1	yes	characteristic
351	C₃₁×#95	C₂³	1	1	yes	characteristic
352	C₃₁×#95	C₂³	1	1	yes	characteristic
353	C₃₁×#95	C₂³	1	1	yes	characteristic
354	C₃₁×#95	C₂³	1	1	yes	characteristic
355	C₃₁×#95	C₂³	1	1	yes	characteristic
356	C₃₁×#95	C₂³	1	1	yes	characteristic
357	C₃₁×#95	C₂³	1	1	yes	characteristic
358	C₃₁×#95	C₂³	1	1	yes	characteristic
359	C₃₁×#95	C₂³	1	1	yes	characteristic
360	C₃₁×#95	C₂³	1	1	yes	characteristic
361	C₃₁×#95	C₂³	1	1	yes	characteristic
362	C₃₁×#95	C₂³	1	1	yes	characteristic
363	C₃₁×#95	C₂³	1	1	yes	characteristic
364	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
365	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
366	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
367	C₂×Q₈×C₃₁	—	4	1	no	—
368	C₂×Q₈×C₃₁	—	4	1	no	—
369	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
370	C₂×D₄×C₃₁	—	4	1	no	—
371	C₂×D₄×C₃₁	—	4	1	no	—
372	C₂×D₄×C₃₁	—	4	1	no	—
373	C₂×D₄×C₃₁	—	4	1	no	—
374	C₂×D₄×C₃₁	—	4	1	no	—
375	C₂×D₄×C₃₁	—	4	1	no	—
376	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
377	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
378	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
379	C₂²×C₄×C₃₁	—	2	2	no	—
380	C₂²×C₄×C₃₁	—	2	2	no	—
381	C₂²×C₄×C₃₁	—	2	2	no	—
382	C₂²×C₄×C₃₁	—	4	1	no	—
383	C₂²×C₄×C₃₁	—	4	1	no	—
384	C₂²×C₄×C₃₁	—	4	1	no	—
385	C₂²×C₄×C₃₁	—	4	1	no	—
386	C₂²×C₄×C₃₁	—	4	1	no	—
387	C₂²×C₄×C₃₁	—	4	1	no	—
388	C₂²×C₄×C₃₁	—	4	1	no	—
389	C₂²×C₄×C₃₁	—	4	1	no	—
390	C₂²×C₄×C₃₁	—	4	1	no	—
391	C₂²×C₄×C₃₁	—	4	1	no	—
392	C₂²×C₄×C₃₁	—	4	1	no	—
393	C₂²×C₄×C₃₁	—	4	1	no	—
394	C₂²×C₄×C₃₁	—	4	1	no	—
395	C₂²×C₄×C₃₁	—	4	1	no	—
396	C₂²×C₄×C₃₁	—	4	1	no	—
397	C₂²×C₄×C₃₁	—	4	1	no	—
398	C₂²×C₄×C₃₁	—	4	1	no	—
399	C₂²×C₄×C₃₁	—	4	1	no	—
400	C₂²×C₄×C₃₁	—	4	1	no	—
401	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
402	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
403	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
404	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
405	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
406	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
410	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
411	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
412	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
413	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
414	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
415	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
416	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
417	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
418	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
419	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
420	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
421	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
422	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
423	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
424	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
425	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
426	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
427	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
428	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
429	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
430	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
431	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
432	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
433	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
434	C₄⋊C₄×C₃₁	—	2	2	no	—
435	C₄⋊C₄×C₃₁	—	2	2	no	—
436	C₄⋊C₄×C₃₁	—	2	2	no	—
437	C₄⋊C₄×C₃₁	—	2	2	no	—
438	C₄⋊C₄×C₃₁	—	2	2	no	—
439	C₄⋊C₄×C₃₁	—	4	1	no	—
440	C₄⋊C₄×C₃₁	—	4	1	no	—
441	C₄⋊C₄×C₃₁	—	4	1	no	—
442	C₄⋊C₄×C₃₁	—	4	1	no	—
443	C₄⋊C₄×C₃₁	—	4	1	no	—
444	C₄⋊C₄×C₃₁	—	4	1	no	—
445	C₄⋊C₄×C₃₁	—	4	1	no	—
446	C₄⋊C₄×C₃₁	—	4	1	no	—
447	C₄⋊C₄×C₃₁	—	4	1	no	—
448	C₄⋊C₄×C₃₁	—	4	1	no	—
449	C₄⋊C₄×C₃₁	—	4	1	no	—
450	C₄⋊C₄×C₃₁	—	4	1	no	—
451	C₄⋊C₄×C₃₁	—	4	1	no	—
452	C₄⋊C₄×C₃₁	—	4	1	no	—
453	C₄⋊C₄×C₃₁	—	4	1	no	—
454	C₄⋊C₄×C₃₁	—	4	1	no	—
455	C₄⋊C₄×C₃₁	—	4	1	no	—
456	C₄⋊C₄×C₃₁	—	4	1	no	—
457	C₄⋊C₄×C₃₁	—	4	1	no	—
458	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
459	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
460	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
461	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
462	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
463	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
464	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
465	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
466	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
467	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
468	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
469	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
470	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
471	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
472	C₂²⋊C₄×C₃₁	—	2	2	no	—
473	C₂²⋊C₄×C₃₁	—	2	2	no	—
474	C₂²⋊C₄×C₃₁	—	2	2	no	—
475	C₂²⋊C₄×C₃₁	—	4	1	no	—
476	C₂²⋊C₄×C₃₁	—	4	1	no	—
477	C₂²⋊C₄×C₃₁	—	4	1	no	—
478	C₂²⋊C₄×C₃₁	—	4	1	no	—
479	C₂²⋊C₄×C₃₁	—	4	1	no	—
480	C₂²⋊C₄×C₃₁	—	4	1	no	—
481	C₂²⋊C₄×C₃₁	—	4	1	no	—
482	C₂²⋊C₄×C₃₁	—	4	1	no	—
483	C₂²⋊C₄×C₃₁	—	4	1	no	—
484	C₂²⋊C₄×C₃₁	—	4	1	no	—
485	C₂²⋊C₄×C₃₁	—	4	1	no	—
486	C₂²⋊C₄×C₃₁	—	4	1	no	—
487	C₂²⋊C₄×C₃₁	—	4	1	no	—
488	C₂²⋊C₄×C₃₁	—	4	1	no	—
489	C₂²⋊C₄×C₃₁	—	4	1	no	—
490	C₂²⋊C₄×C₃₁	—	4	1	no	—
491	C₂²⋊C₄×C₃₁	—	4	1	no	—
492	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
493	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
494	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
495	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
496	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
497	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
498	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
499	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
500	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
501	C₂²⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
502	C₄²×C₃₁	—	2	2	no	—
503	C₄²×C₃₁	—	2	2	no	—
504	C₄²×C₃₁	—	2	2	no	—
505	C₄²×C₃₁	—	4	1	no	—
506	C₄²×C₃₁	—	4	1	no	—
507	C₄²×C₃₁	—	4	1	no	—
508	C₄²×C₃₁	—	4	1	no	—
509	C₄²×C₃₁	—	4	1	no	—
510	C₄²×C₃₁	—	4	1	no	—
511	C₄²×C₃₁	—	4	1	no	—
512	C₄²×C₃₁	—	4	1	no	—
513	C₄²×C₃₁	—	4	1	no	—
514	C₄²×C₃₁	—	4	1	no	—
515	C₄²×C₃₁	—	4	1	no	—
516	C₄²×C₃₁	—	4	1	no	—
517	C₄²×C₃₁	—	4	1	no	—
518	C₄²×C₃₁	—	4	1	no	—
519	C₄²×C₃₁	—	4	1	no	—
520	C₄²×C₃₁	—	4	1	no	—
521	C₄²×C₃₁	—	4	1	no	—
522	C₄²×C₃₁	—	4	1	no	—
523	C₄²×C₃₁	—	4	1	no	—
524	C₄²×C₃₁	—	4	1	no	—
525	C₄²×C₃₁	—	4	1	no	—
526	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
527	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
528	#34449	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
529	C₂³×C₃₁	—	2	1	no	—
530	C₂³×C₃₁	—	2	1	no	—
531	C₂³×C₃₁	—	2	1	no	—
532	C₂³×C₃₁	—	2	1	no	—
533	C₂³×C₃₁	—	2	1	no	—
534	C₂³×C₃₁	—	2	1	no	—
535	C₂³×C₃₁	—	2	1	no	—
536	C₂³×C₃₁	—	2	1	no	—
537	C₂³×C₃₁	—	2	1	no	—
538	C₂³×C₃₁	—	2	1	no	—
539	C₂³×C₃₁	—	2	1	no	—
540	C₂³×C₃₁	—	2	1	no	—
541	C₂³×C₃₁	—	2	1	no	—
542	C₂³×C₃₁	—	2	1	no	—
543	C₂³×C₃₁	—	2	1	no	—
544	C₂³×C₃₁	—	2	1	no	—
545	C₂³×C₃₁	—	2	1	no	—
546	C₂³×C₃₁	—	2	1	no	—
547	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
548	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
549	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
550	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
551	Q₈×C₃₁	—	4	4	no	—
552	D₄×C₃₁	—	4	4	no	—
553	D₄×C₃₁	—	4	4	no	—
554	D₄×C₃₁	—	4	4	no	—
555	C₂×C₄×C₃₁	—	2	1	no	—
556	C₂×C₄×C₃₁	—	2	1	no	—
557	C₂×C₄×C₃₁	—	2	1	no	—
558	C₂×C₄×C₃₁	—	2	1	no	—
559	C₂×C₄×C₃₁	—	2	1	no	—
560	C₂×C₄×C₃₁	—	2	1	no	—
561	C₂×C₄×C₃₁	—	2	1	no	—
562	C₂×C₄×C₃₁	—	2	1	no	—
563	C₂×C₄×C₃₁	—	2	1	no	—
564	C₂×C₄×C₃₁	—	2	1	no	—
565	C₂×C₄×C₃₁	—	2	1	no	—
566	C₂×C₄×C₃₁	—	2	1	no	—
567	C₂×C₄×C₃₁	—	2	1	no	—
568	C₂×C₄×C₃₁	—	2	1	no	—
569	C₂×C₄×C₃₁	—	2	1	no	—
570	C₂×C₄×C₃₁	—	2	1	no	—
571	C₂×C₄×C₃₁	—	2	1	no	—
572	C₂×C₄×C₃₁	—	2	1	no	—
573	C₂×C₄×C₃₁	—	2	1	no	—
574	C₂×C₄×C₃₁	—	2	1	no	—
575	C₂×C₄×C₃₁	—	2	1	no	—
576	C₂×C₄×C₃₁	—	2	1	no	—
577	C₂×C₄×C₃₁	—	2	1	no	—
578	C₂×C₄×C₃₁	—	2	1	no	—
579	C₂×C₄×C₃₁	—	2	1	no	—
580	C₂×C₄×C₃₁	—	2	1	no	—
581	C₂×C₄×C₃₁	—	2	1	no	—
582	C₂×C₄×C₃₁	—	2	1	no	—
583	C₂×C₄×C₃₁	—	2	1	no	—
584	C₂×C₄×C₃₁	—	2	1	no	—
585	C₂×C₄×C₃₁	—	2	1	no	—
586	C₂×C₄×C₃₁	—	2	1	no	—
587	C₂×C₄×C₃₁	—	2	1	no	—
588	C₂×C₄×C₃₁	—	2	1	no	—
589	C₂×C₄×C₃₁	—	2	1	no	—
590	C₂×C₄×C₃₁	—	2	1	no	—
591	C₂×C₄×C₃₁	—	2	1	no	—
592	C₂×C₄×C₃₁	—	2	1	no	—
593	C₂×C₄×C₃₁	—	2	1	no	—
594	C₂×C₄×C₃₁	—	2	1	no	—
595	C₂×C₄×C₃₁	—	2	1	no	—
596	C₂×C₄×C₃₁	—	2	1	no	—
597	C₂×C₄×C₃₁	—	2	1	no	—
598	C₂×C₄×C₃₁	—	2	1	no	—
599	C₂×C₄×C₃₁	—	2	1	no	—
600	C₂×C₄×C₃₁	—	2	1	no	—
601	C₂×C₄×C₃₁	—	2	1	no	—
602	C₂×C₄×C₃₁	—	2	1	no	—
603	C₂×C₄×C₃₁	—	2	1	no	—
604	C₂×C₄×C₃₁	—	2	1	no	—
605	C₂×C₄×C₃₁	—	2	1	no	—
606	C₂×C₄×C₃₁	—	2	1	no	—
607	C₂×C₄×C₃₁	—	2	1	no	—
608	C₂×C₄×C₃₁	—	2	1	no	—
609	C₂×C₄×C₃₁	—	2	1	no	—
610	C₂×C₄×C₃₁	—	2	1	no	—
611	C₂×C₄×C₃₁	—	2	1	no	—
612	C₂×C₄×C₃₁	—	2	1	no	—
613	C₂×C₄×C₃₁	—	2	1	no	—
614	C₂×C₄×C₃₁	—	2	1	no	—
615	C₂×C₄×C₃₁	—	2	1	no	—
616	C₂×C₄×C₃₁	—	2	1	no	—
617	C₂×C₄×C₃₁	—	2	1	no	—
618	C₂×C₄×C₃₁	—	2	1	no	—
619	C₂×C₄×C₃₁	—	2	1	no	—
620	C₂×C₄×C₃₁	—	2	1	no	—
621	C₂×C₄×C₃₁	—	2	1	no	—
622	C₂×C₄×C₃₁	—	2	1	no	—
623	C₂×C₄×C₃₁	—	2	1	no	—
624	C₂×C₄×C₃₁	—	2	1	no	—
625	C₂×C₄×C₃₁	—	4	4	no	—
626	C₂×C₄×C₃₁	—	4	4	no	—
627	C₂×C₄×C₃₁	—	4	4	no	—
628	C₂×C₄×C₃₁	—	4	4	no	—
629	C₂×C₄×C₃₁	—	4	4	no	—
630	C₂×C₄×C₃₁	—	4	4	no	—
631	C₂×C₄×C₃₁	—	4	4	no	—
632	C₂×C₄×C₃₁	—	8	2	no	—
633	C₂×C₄×C₃₁	—	8	2	no	—
634	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
635	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
636	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
637	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
638	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
639	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
640	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
641	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
642	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
643	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
644	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
645	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
646	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
647	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
648	C₂×#539	C₂×C₃₁	1	1	yes	characteristic
649	#2382	C₂×C₃₁	1	1	yes	characteristic, complemented
650	#2378	C₂×C₃₁	1	1	yes	characteristic, complemented
651	#2378	C₂×C₃₁	1	1	yes	characteristic, complemented
652	#2376	C₂×C₃₁	1	1	yes	characteristic, complemented
653	#2374	C₂×C₃₁	1	1	yes	characteristic, complemented
654	#2373	C₂×C₃₁	1	1	yes	characteristic, complemented
655	#2373	C₂×C₃₁	1	1	yes	characteristic, complemented
656	#2371	C₂×C₃₁	1	1	yes	characteristic, complemented
657	#2370	C₂×C₃₁	1	1	yes	characteristic, complemented
658	#2370	C₂×C₃₁	1	1	yes	characteristic, complemented
659	#2362	C₂×C₃₁	1	1	yes	characteristic, complemented
660	#2360	C₂×C₃₁	1	1	yes	characteristic, complemented
661	#2357	C₂×C₃₁	1	1	yes	characteristic, complemented
662	#2352	C₂×C₃₁	1	1	yes	characteristic, complemented
663	#2345	C₂×C₃₁	1	1	yes	characteristic, complemented
664	#2344	C₂×C₃₁	1	1	yes	characteristic, complemented
665	#2335	C₂×C₃₁	1	1	yes	characteristic, complemented
666	#2335	C₂×C₃₁	1	1	yes	characteristic, complemented
667	#2335	C₂×C₃₁	1	1	yes	characteristic, complemented
668	#2335	C₂×C₃₁	1	1	yes	characteristic, complemented
669	#2334	C₂×C₃₁	1	1	yes	characteristic, complemented
670	#2334	C₂×C₃₁	1	1	yes	characteristic, complemented
671	#2333	C₂×C₃₁	1	1	yes	characteristic
672	#2332	C₂×C₃₁	1	1	yes	characteristic, complemented
673	#2324	C₂×C₃₁	1	1	yes	characteristic
674	#2322	C₂×C₃₁	1	1	yes	characteristic, complemented
675	#2319	C₂×C₃₁	1	1	yes	characteristic, complemented
676	C₄×C₂²⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
677	C₄×#123	C₂×C₃₁	1	1	yes	characteristic, complemented
678	#2290	C₂×C₃₁	1	1	yes	characteristic, complemented
679	C₂²×C₃₁	—	2	2	no	—
680	C₂²×C₃₁	—	2	2	no	—
681	C₂²×C₃₁	—	2	2	no	—
682	C₂²×C₃₁	—	2	2	no	—
683	C₂²×C₃₁	—	2	2	no	—
684	C₂²×C₃₁	—	2	2	no	—
685	C₂²×C₃₁	—	2	2	no	—
686	C₂²×C₃₁	—	2	2	no	—
687	C₂²×C₃₁	—	2	2	no	—
688	C₂²×C₃₁	—	4	1	no	—
689	C₂²×C₃₁	—	4	1	no	—
690	C₂²×C₃₁	—	4	1	no	—
691	C₂²×C₃₁	—	4	1	no	—
692	C₂²×C₃₁	—	4	1	no	—
693	C₂²×C₃₁	—	4	1	no	—
694	C₂²×C₃₁	—	4	1	no	—
695	C₂²×C₃₁	—	4	1	no	—
696	C₂²×C₃₁	—	4	1	no	—
697	C₂²×C₃₁	—	4	1	no	—
698	C₂²×C₃₁	—	4	1	no	—
699	C₂²×C₃₁	—	4	1	no	—
700	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
701	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
702	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
703	C₂²×C₃₁	#585	1	1	yes	characteristic
704	C₂²×C₃₁	#585	1	1	yes	characteristic
705	C₂²×C₃₁	#585	1	1	yes	characteristic
706	C₂²×C₃₁	#585	1	1	yes	characteristic
707	C₄×C₃₁	—	2	2	no	—
708	C₄×C₃₁	—	2	2	no	—
709	C₄×C₃₁	—	2	2	no	—
710	C₄×C₃₁	—	2	2	no	—
711	C₄×C₃₁	—	2	2	no	—
712	C₄×C₃₁	—	2	2	no	—
713	C₄×C₃₁	—	2	2	no	—
714	C₄×C₃₁	—	2	2	no	—
715	C₄×C₃₁	—	2	2	no	—
716	C₄×C₃₁	—	2	2	no	—
717	C₄×C₃₁	—	2	2	no	—
718	C₄×C₃₁	—	2	2	no	—
719	C₄×C₃₁	—	2	2	no	—
720	C₄×C₃₁	—	2	2	no	—
721	C₄×C₃₁	—	4	1	no	—
722	C₄×C₃₁	—	4	1	no	—
723	C₄×C₃₁	—	4	1	no	—
724	C₄×C₃₁	—	4	1	no	—
725	C₄×C₃₁	—	4	1	no	—
726	C₄×C₃₁	—	4	1	no	—
727	C₄×C₃₁	—	4	1	no	—
728	C₄×C₃₁	—	4	1	no	—
729	C₄×C₃₁	—	4	1	no	—
730	C₄×C₃₁	—	4	1	no	—
731	C₄×C₃₁	—	4	1	no	—
732	C₄×C₃₁	—	4	1	no	—
733	C₄×C₃₁	—	4	1	no	—
734	C₄×C₃₁	—	4	1	no	—
735	#539	C₄×C₃₁	1	16	yes	complemented
736	C₂×#126	C₂²×C₃₁	1	1	yes	characteristic
737	C₂×#126	C₂²×C₃₁	1	1	yes	characteristic
738	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
739	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
740	C₂×#123	C₂²×C₃₁	1	1	yes	characteristic
741	C₂×#123	C₂²×C₃₁	1	1	yes	characteristic
742	C₂×#123	C₂²×C₃₁	1	1	yes	characteristic
743	C₂×#123	C₂²×C₃₁	1	1	yes	characteristic
744	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
745	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
746	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
747	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
748	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
749	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
750	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
751	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
752	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
753	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
754	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
755	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
756	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
757	#391	C₂²×C₃₁	1	1	yes	characteristic
758	#391	C₂²×C₃₁	1	1	yes	characteristic
759	#391	C₂²×C₃₁	1	1	yes	characteristic
760	#390	C₂²×C₃₁	1	1	yes	characteristic
761	#390	C₂²×C₃₁	1	1	yes	characteristic
762	#390	C₂²×C₃₁	1	1	yes	characteristic
763	#390	C₂²×C₃₁	1	1	yes	characteristic
764	#390	C₂²×C₃₁	1	1	yes	characteristic
765	#389	C₂²×C₃₁	1	1	yes	characteristic
766	#389	C₂²×C₃₁	1	1	yes	characteristic
767	#389	C₂²×C₃₁	1	1	yes	characteristic
768	#389	C₂²×C₃₁	1	1	yes	characteristic
769	#389	C₂²×C₃₁	1	1	yes	characteristic
770	#389	C₂²×C₃₁	1	1	yes	characteristic
771	#389	C₂²×C₃₁	1	1	yes	characteristic
772	#389	C₂²×C₃₁	1	1	yes	characteristic
773	#389	C₂²×C₃₁	1	1	yes	characteristic
774	#389	C₂²×C₃₁	1	1	yes	characteristic
775	#389	C₂²×C₃₁	1	1	yes	characteristic
776	#389	C₂²×C₃₁	1	1	yes	characteristic
777	#389	C₂²×C₃₁	1	1	yes	characteristic
778	#389	C₂²×C₃₁	1	1	yes	characteristic
779	#388	C₂²×C₃₁	1	1	yes	characteristic
780	#388	C₂²×C₃₁	1	1	yes	characteristic
781	#388	C₂²×C₃₁	1	1	yes	characteristic
782	#388	C₂²×C₃₁	1	1	yes	characteristic
783	#388	C₂²×C₃₁	1	1	yes	characteristic
784	#388	C₂²×C₃₁	1	1	yes	characteristic
785	#388	C₂²×C₃₁	1	1	yes	characteristic
786	#388	C₂²×C₃₁	1	1	yes	characteristic
787	#388	C₂²×C₃₁	1	1	yes	characteristic
788	#388	C₂²×C₃₁	1	1	yes	characteristic
789	#388	C₂²×C₃₁	1	1	yes	characteristic
790	#388	C₂²×C₃₁	1	1	yes	characteristic
791	#388	C₂²×C₃₁	1	1	yes	characteristic
792	#388	C₂²×C₃₁	1	1	yes	characteristic
793	#388	C₂²×C₃₁	1	1	yes	characteristic
794	#388	C₂²×C₃₁	1	1	yes	characteristic
795	#388	C₂²×C₃₁	1	1	yes	characteristic
796	#388	C₂²×C₃₁	1	1	yes	characteristic
797	#388	C₂²×C₃₁	1	1	yes	characteristic
798	#388	C₂²×C₃₁	1	1	yes	characteristic
799	#388	C₂²×C₃₁	1	1	yes	characteristic
800	#388	C₂²×C₃₁	1	1	yes	characteristic
801	#388	C₂²×C₃₁	1	1	yes	characteristic
802	#388	C₂²×C₃₁	1	1	yes	characteristic
803	#387	C₂²×C₃₁	1	1	yes	characteristic
804	#387	C₂²×C₃₁	1	1	yes	characteristic
805	#387	C₂²×C₃₁	1	1	yes	characteristic
806	#387	C₂²×C₃₁	1	1	yes	characteristic
807	#387	C₂²×C₃₁	1	1	yes	characteristic
808	#387	C₂²×C₃₁	1	1	yes	characteristic
809	#387	C₂²×C₃₁	1	1	yes	characteristic
810	#387	C₂²×C₃₁	1	1	yes	characteristic
811	#387	C₂²×C₃₁	1	1	yes	characteristic
812	#387	C₂²×C₃₁	1	1	yes	characteristic
813	#387	C₂²×C₃₁	1	1	yes	characteristic
814	#387	C₂²×C₃₁	1	1	yes	characteristic
815	#387	C₂²×C₃₁	1	1	yes	characteristic
816	#387	C₂²×C₃₁	1	1	yes	characteristic
817	#387	C₂²×C₃₁	1	1	yes	characteristic
818	#387	C₂²×C₃₁	1	1	yes	characteristic
819	#387	C₂²×C₃₁	1	1	yes	characteristic
820	#387	C₂²×C₃₁	1	1	yes	characteristic
821	#387	C₂²×C₃₁	1	1	yes	characteristic
822	#387	C₂²×C₃₁	1	1	yes	characteristic
823	#387	C₂²×C₃₁	1	1	yes	characteristic
824	#387	C₂²×C₃₁	1	1	yes	characteristic
825	#387	C₂²×C₃₁	1	1	yes	characteristic
826	#387	C₂²×C₃₁	1	1	yes	characteristic
827	#387	C₂²×C₃₁	1	1	yes	characteristic
828	#387	C₂²×C₃₁	1	1	yes	characteristic
829	#387	C₂²×C₃₁	1	1	yes	characteristic
830	#387	C₂²×C₃₁	1	1	yes	characteristic
831	#386	C₂²×C₃₁	1	1	yes	characteristic
832	#386	C₂²×C₃₁	1	1	yes	characteristic
833	#386	C₂²×C₃₁	1	1	yes	characteristic
834	#386	C₂²×C₃₁	1	1	yes	characteristic
835	#386	C₂²×C₃₁	1	1	yes	characteristic
836	#386	C₂²×C₃₁	1	1	yes	characteristic
837	#385	C₂²×C₃₁	1	1	yes	characteristic
838	#385	C₂²×C₃₁	1	1	yes	characteristic
839	#385	C₂²×C₃₁	1	1	yes	characteristic
840	#385	C₂²×C₃₁	1	1	yes	characteristic
841	#385	C₂²×C₃₁	1	1	yes	characteristic
842	#385	C₂²×C₃₁	1	1	yes	characteristic
843	#385	C₂²×C₃₁	1	1	yes	characteristic
844	#385	C₂²×C₃₁	1	1	yes	characteristic
845	#382	C₂²×C₃₁	1	1	yes	characteristic
846	#382	C₂²×C₃₁	1	1	yes	characteristic
847	#381	C₂²×C₃₁	1	1	yes	characteristic
848	#381	C₂²×C₃₁	1	1	yes	characteristic
849	#381	C₂²×C₃₁	1	1	yes	characteristic
850	#381	C₂²×C₃₁	1	1	yes	characteristic
851	#380	C₂²×C₃₁	1	1	yes	characteristic
852	#380	C₂²×C₃₁	1	1	yes	characteristic
853	#380	C₂²×C₃₁	1	1	yes	characteristic
854	#380	C₂²×C₃₁	1	1	yes	characteristic
855	#380	C₂²×C₃₁	1	1	yes	characteristic
856	#380	C₂²×C₃₁	1	1	yes	characteristic
857	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
858	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
859	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
860	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
861	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
862	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
863	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
864	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
865	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
866	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
867	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
868	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
869	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
870	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
871	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
872	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
873	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
874	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
875	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
876	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
877	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
878	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
879	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
880	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
881	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
882	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
883	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
884	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
885	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
886	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
887	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
888	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
889	#376	C₂²×C₃₁	1	1	yes	characteristic
890	#376	C₂²×C₃₁	1	1	yes	characteristic
891	C₂×C₃₁	—	4	2	no	—
892	C₂×C₃₁	—	4	2	no	—
893	C₂×C₃₁	—	4	2	no	—
894	C₂×C₃₁	#3428	1	1	yes	characteristic
895	C₂×C₃₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
896	C₂×C₃₁	C₄×2₋¹⁺⁴	1	1	yes	characteristic
897	C₂×C₃₁	#3533	1	1	yes	characteristic
898	C₂×C₃₁	#3541	1	1	yes	characteristic
899	C₂×C₃₁	#3557	1	1	yes	characteristic
900	C₂×C₃₁	#3567	1	1	yes	characteristic
901	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
902	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
903	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
904	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
905	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
906	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
907	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
908	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
909	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
910	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
911	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
912	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
913	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
914	#126	C₂×C₄×C₃₁	1	8	yes	complemented
915	#126	C₂×C₄×C₃₁	1	8	yes	complemented
916	#125	C₂×C₄×C₃₁	1	8	yes	complemented
917	#125	C₂×C₄×C₃₁	1	8	yes	complemented
918	#123	C₂×C₄×C₃₁	1	8	yes	—
919	#123	C₂×C₄×C₃₁	1	8	yes	—
920	#123	C₂×C₄×C₃₁	1	8	yes	complemented
921	#123	C₂×C₄×C₃₁	1	8	yes	complemented
922	C₂²⋊Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
923	C₂²⋊Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
924	C₂²⋊Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
925	#121	C₂×C₄×C₃₁	1	8	yes	—
926	C₄×Q₈	—	4	2	no	—
927	C₄×D₄	—	4	2	no	—
928	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
929	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
930	#117	—	4	2	no	—
931	#117	—	4	2	no	—
932	C₂×C₄⋊C₄	—	4	2	no	—
933	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	8	yes	complemented
934	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
935	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
936	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
937	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
938	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
939	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
940	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
941	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
942	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
943	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
944	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
945	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
946	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
947	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
948	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
949	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
950	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
951	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
952	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
953	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
954	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
955	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
956	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
957	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
958	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
959	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
960	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
961	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
962	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
963	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
964	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
965	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
966	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
967	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
968	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
969	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
970	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
971	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
972	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
973	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
974	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
975	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
976	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
977	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
978	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
979	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
980	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
981	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
982	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
983	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
984	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
985	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
986	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
987	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
988	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
989	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
990	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
991	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
992	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
993	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
994	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
995	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
996	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
997	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
998	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
999	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1000	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1001	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1002	C₂×C₄²	—	4	2	no	—
1003	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1004	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1005	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1006	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1007	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1008	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1009	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1010	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1011	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1012	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1013	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1014	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1015	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1016	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1017	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1018	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1019	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1020	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1021	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1022	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1023	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1024	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1025	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1026	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1027	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1028	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1029	#95	C₂³×C₃₁	1	1	yes	characteristic
1030	#95	C₂³×C₃₁	1	1	yes	characteristic
1031	#95	C₂³×C₃₁	1	1	yes	characteristic
1032	#95	C₂³×C₃₁	1	1	yes	characteristic
1033	#95	C₂³×C₃₁	1	1	yes	characteristic
1034	#95	C₂³×C₃₁	1	1	yes	characteristic
1035	#95	C₂³×C₃₁	1	1	yes	characteristic
1036	#95	C₂³×C₃₁	1	1	yes	characteristic
1037	#95	C₂³×C₃₁	1	1	yes	characteristic
1038	#95	C₂³×C₃₁	1	1	yes	characteristic
1039	#95	C₂³×C₃₁	1	1	yes	characteristic
1040	#95	C₂³×C₃₁	1	1	yes	characteristic
1041	#95	C₂³×C₃₁	1	1	yes	characteristic
1042	#95	C₂³×C₃₁	1	1	yes	characteristic
1043	#95	C₂³×C₃₁	1	1	yes	characteristic
1044	#95	C₂³×C₃₁	1	1	yes	characteristic
1045	#95	C₂³×C₃₁	1	1	yes	characteristic
1046	#95	C₂³×C₃₁	1	1	yes	characteristic
1047	#95	C₂³×C₃₁	1	1	yes	characteristic
1048	#95	C₂³×C₃₁	1	1	yes	characteristic
1049	#95	C₂³×C₃₁	1	1	yes	characteristic
1050	#95	C₂³×C₃₁	1	1	yes	characteristic
1051	#95	C₂³×C₃₁	1	1	yes	characteristic
1052	#95	C₂³×C₃₁	1	1	yes	characteristic
1053	#95	C₂³×C₃₁	1	1	yes	characteristic
1054	#95	C₂³×C₃₁	1	1	yes	characteristic
1055	#95	C₂³×C₃₁	1	1	yes	characteristic
1056	#95	C₂³×C₃₁	1	1	yes	characteristic
1057	#95	C₂³×C₃₁	1	1	yes	characteristic
1058	#95	C₂³×C₃₁	1	1	yes	characteristic
1059	#95	C₂³×C₃₁	1	1	yes	characteristic
1060	#95	C₂³×C₃₁	1	1	yes	characteristic
1061	#95	C₂³×C₃₁	1	1	yes	characteristic
1062	#95	C₂³×C₃₁	1	1	yes	characteristic
1063	#95	C₂³×C₃₁	1	1	yes	characteristic
1064	#95	C₂³×C₃₁	1	1	yes	characteristic
1065	#95	C₂³×C₃₁	1	1	yes	characteristic
1066	#95	C₂³×C₃₁	1	1	yes	characteristic
1067	#95	C₂³×C₃₁	1	1	yes	characteristic
1068	#95	C₂³×C₃₁	1	1	yes	characteristic
1069	#95	C₂³×C₃₁	1	1	yes	characteristic
1070	#95	C₂³×C₃₁	1	1	yes	characteristic
1071	#95	C₂³×C₃₁	1	1	yes	characteristic
1072	#95	C₂³×C₃₁	1	1	yes	characteristic
1073	#95	C₂³×C₃₁	1	1	yes	characteristic
1074	#95	C₂³×C₃₁	1	1	yes	characteristic
1075	#95	C₂³×C₃₁	1	1	yes	characteristic
1076	#95	C₂³×C₃₁	1	1	yes	characteristic
1077	C₃₁	#34449	1	1	yes	characteristic, direct product factor, Sylow
1078	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
1079	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
1080	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
1081	C₂×Q₈	—	4	1	no	—
1082	C₂×Q₈	—	4	1	no	—
1083	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
1084	C₂×D₄	—	4	1	no	—
1085	C₂×D₄	—	4	1	no	—
1086	C₂×D₄	—	4	1	no	—
1087	C₂×D₄	—	4	1	no	—
1088	C₂×D₄	—	4	1	no	—
1089	C₂×D₄	—	4	1	no	—
1090	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
1091	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
1092	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
1093	C₂²×C₄	—	2	2	no	—
1094	C₂²×C₄	—	2	2	no	—
1095	C₂²×C₄	—	2	2	no	—
1096	C₂²×C₄	—	4	1	no	—
1097	C₂²×C₄	—	4	1	no	—
1098	C₂²×C₄	—	4	1	no	—
1099	C₂²×C₄	—	4	1	no	—
1100	C₂²×C₄	—	4	1	no	—
1101	C₂²×C₄	—	4	1	no	—
1102	C₂²×C₄	—	4	1	no	—
1103	C₂²×C₄	—	4	1	no	—
1104	C₂²×C₄	—	4	1	no	—
1105	C₂²×C₄	—	4	1	no	—
1106	C₂²×C₄	—	4	1	no	—
1107	C₂²×C₄	—	4	1	no	—
1108	C₂²×C₄	—	4	1	no	—
1109	C₂²×C₄	—	4	1	no	—
1110	C₂²×C₄	—	4	1	no	—
1111	C₂²×C₄	—	4	1	no	—
1112	C₂²×C₄	—	4	1	no	—
1113	C₂²×C₄	—	4	1	no	—
1114	C₂²×C₄	—	4	1	no	—
1115	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
1116	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
1117	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
1118	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
1119	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
1120	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1121	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1122	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1123	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1124	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1125	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1126	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1127	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1128	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1129	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1130	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1131	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1132	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1133	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1134	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1135	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1136	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1137	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1138	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1139	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1140	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1141	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1142	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1143	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1144	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1145	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1146	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1147	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1148	C₄⋊C₄	—	2	2	no	—
1149	C₄⋊C₄	—	2	2	no	—
1150	C₄⋊C₄	—	2	2	no	—
1151	C₄⋊C₄	—	2	2	no	—
1152	C₄⋊C₄	—	2	2	no	—
1153	C₄⋊C₄	—	4	1	no	—
1154	C₄⋊C₄	—	4	1	no	—
1155	C₄⋊C₄	—	4	1	no	—
1156	C₄⋊C₄	—	4	1	no	—
1157	C₄⋊C₄	—	4	1	no	—
1158	C₄⋊C₄	—	4	1	no	—
1159	C₄⋊C₄	—	4	1	no	—
1160	C₄⋊C₄	—	4	1	no	—
1161	C₄⋊C₄	—	4	1	no	—
1162	C₄⋊C₄	—	4	1	no	—
1163	C₄⋊C₄	—	4	1	no	—
1164	C₄⋊C₄	—	4	1	no	—
1165	C₄⋊C₄	—	4	1	no	—
1166	C₄⋊C₄	—	4	1	no	—
1167	C₄⋊C₄	—	4	1	no	—
1168	C₄⋊C₄	—	4	1	no	—
1169	C₄⋊C₄	—	4	1	no	—
1170	C₄⋊C₄	—	4	1	no	—
1171	C₄⋊C₄	—	4	1	no	—
1172	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1173	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1174	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1175	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1176	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1177	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1178	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1179	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1180	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1181	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1182	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1183	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1184	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1185	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1186	C₂²⋊C₄	—	2	2	no	—
1187	C₂²⋊C₄	—	2	2	no	—
1188	C₂²⋊C₄	—	2	2	no	—
1189	C₂²⋊C₄	—	4	1	no	—
1190	C₂²⋊C₄	—	4	1	no	—
1191	C₂²⋊C₄	—	4	1	no	—
1192	C₂²⋊C₄	—	4	1	no	—
1193	C₂²⋊C₄	—	4	1	no	—
1194	C₂²⋊C₄	—	4	1	no	—
1195	C₂²⋊C₄	—	4	1	no	—
1196	C₂²⋊C₄	—	4	1	no	—
1197	C₂²⋊C₄	—	4	1	no	—
1198	C₂²⋊C₄	—	4	1	no	—
1199	C₂²⋊C₄	—	4	1	no	—
1200	C₂²⋊C₄	—	4	1	no	—
1201	C₂²⋊C₄	—	4	1	no	—
1202	C₂²⋊C₄	—	4	1	no	—
1203	C₂²⋊C₄	—	4	1	no	—
1204	C₂²⋊C₄	—	4	1	no	—
1205	C₂²⋊C₄	—	4	1	no	—
1206	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1207	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1208	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1209	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1210	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1211	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1212	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1213	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1214	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1215	C₂²⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
1216	C₄²	—	2	2	no	—
1217	C₄²	—	2	2	no	—
1218	C₄²	—	2	2	no	—
1219	C₄²	—	4	1	no	—
1220	C₄²	—	4	1	no	—
1221	C₄²	—	4	1	no	—
1222	C₄²	—	4	1	no	—
1223	C₄²	—	4	1	no	—
1224	C₄²	—	4	1	no	—
1225	C₄²	—	4	1	no	—
1226	C₄²	—	4	1	no	—
1227	C₄²	—	4	1	no	—
1228	C₄²	—	4	1	no	—
1229	C₄²	—	4	1	no	—
1230	C₄²	—	4	1	no	—
1231	C₄²	—	4	1	no	—
1232	C₄²	—	4	1	no	—
1233	C₄²	—	4	1	no	—
1234	C₄²	—	4	1	no	—
1235	C₄²	—	4	1	no	—
1236	C₄²	—	4	1	no	—
1237	C₄²	—	4	1	no	—
1238	C₄²	—	4	1	no	—
1239	C₄²	—	4	1	no	—
1240	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
1241	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
1242	C₂³	—	2	1	no	—
1243	C₂³	—	2	1	no	—
1244	C₂³	—	2	1	no	—
1245	C₂³	—	2	1	no	—
1246	C₂³	—	2	1	no	—
1247	C₂³	—	2	1	no	—
1248	C₂³	—	2	1	no	—
1249	C₂³	—	2	1	no	—
1250	C₂³	—	2	1	no	—
1251	C₂³	—	2	1	no	—
1252	C₂³	—	2	1	no	—
1253	C₂³	—	2	1	no	—
1254	C₂³	—	2	1	no	—
1255	C₂³	—	2	1	no	—
1256	C₂³	—	2	1	no	—
1257	C₂³	—	2	1	no	—
1258	C₂³	—	2	1	no	—
1259	C₂³	—	2	1	no	—
1260	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
1261	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
1262	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
1263	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
1264	Q₈	—	4	4	no	—
1265	D₄	—	4	4	no	—
1266	D₄	—	4	4	no	—
1267	D₄	—	4	4	no	—
1268	C₂×C₄	—	2	1	no	—
1269	C₂×C₄	—	2	1	no	—
1270	C₂×C₄	—	2	1	no	—
1271	C₂×C₄	—	2	1	no	—
1272	C₂×C₄	—	2	1	no	—
1273	C₂×C₄	—	2	1	no	—
1274	C₂×C₄	—	2	1	no	—
1275	C₂×C₄	—	2	1	no	—
1276	C₂×C₄	—	2	1	no	—
1277	C₂×C₄	—	2	1	no	—
1278	C₂×C₄	—	2	1	no	—
1279	C₂×C₄	—	2	1	no	—
1280	C₂×C₄	—	2	1	no	—
1281	C₂×C₄	—	2	1	no	—
1282	C₂×C₄	—	2	1	no	—
1283	C₂×C₄	—	2	1	no	—
1284	C₂×C₄	—	2	1	no	—
1285	C₂×C₄	—	2	1	no	—
1286	C₂×C₄	—	2	1	no	—
1287	C₂×C₄	—	2	1	no	—
1288	C₂×C₄	—	2	1	no	—
1289	C₂×C₄	—	2	1	no	—
1290	C₂×C₄	—	2	1	no	—
1291	C₂×C₄	—	2	1	no	—
1292	C₂×C₄	—	2	1	no	—
1293	C₂×C₄	—	2	1	no	—
1294	C₂×C₄	—	2	1	no	—
1295	C₂×C₄	—	2	1	no	—
1296	C₂×C₄	—	2	1	no	—
1297	C₂×C₄	—	2	1	no	—
1298	C₂×C₄	—	2	1	no	—
1299	C₂×C₄	—	2	1	no	—
1300	C₂×C₄	—	2	1	no	—
1301	C₂×C₄	—	2	1	no	—
1302	C₂×C₄	—	2	1	no	—
1303	C₂×C₄	—	2	1	no	—
1304	C₂×C₄	—	2	1	no	—
1305	C₂×C₄	—	2	1	no	—
1306	C₂×C₄	—	2	1	no	—
1307	C₂×C₄	—	2	1	no	—
1308	C₂×C₄	—	2	1	no	—
1309	C₂×C₄	—	2	1	no	—
1310	C₂×C₄	—	2	1	no	—
1311	C₂×C₄	—	2	1	no	—
1312	C₂×C₄	—	2	1	no	—
1313	C₂×C₄	—	2	1	no	—
1314	C₂×C₄	—	2	1	no	—
1315	C₂×C₄	—	2	1	no	—
1316	C₂×C₄	—	2	1	no	—
1317	C₂×C₄	—	2	1	no	—
1318	C₂×C₄	—	2	1	no	—
1319	C₂×C₄	—	2	1	no	—
1320	C₂×C₄	—	2	1	no	—
1321	C₂×C₄	—	2	1	no	—
1322	C₂×C₄	—	2	1	no	—
1323	C₂×C₄	—	2	1	no	—
1324	C₂×C₄	—	2	1	no	—
1325	C₂×C₄	—	2	1	no	—
1326	C₂×C₄	—	2	1	no	—
1327	C₂×C₄	—	2	1	no	—
1328	C₂×C₄	—	2	1	no	—
1329	C₂×C₄	—	2	1	no	—
1330	C₂×C₄	—	2	1	no	—
1331	C₂×C₄	—	2	1	no	—
1332	C₂×C₄	—	2	1	no	—
1333	C₂×C₄	—	2	1	no	—
1334	C₂×C₄	—	2	1	no	—
1335	C₂×C₄	—	2	1	no	—
1336	C₂×C₄	—	2	1	no	—
1337	C₂×C₄	—	2	1	no	—
1338	C₂×C₄	—	4	4	no	—
1339	C₂×C₄	—	4	4	no	—
1340	C₂×C₄	—	4	4	no	—
1341	C₂×C₄	—	4	4	no	—
1342	C₂×C₄	—	4	4	no	—
1343	C₂×C₄	—	4	4	no	—
1344	C₂×C₄	—	4	4	no	—
1345	C₂×C₄	—	8	2	no	—
1346	C₂×C₄	—	8	2	no	—
1347	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1348	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1349	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1350	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1351	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1352	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1353	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1354	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1355	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1356	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1357	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1358	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
1359	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1360	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1361	C₂²	—	2	2	no	—
1362	C₂²	—	2	2	no	—
1363	C₂²	—	2	2	no	—
1364	C₂²	—	2	2	no	—
1365	C₂²	—	2	2	no	—
1366	C₂²	—	2	2	no	—
1367	C₂²	—	2	2	no	—
1368	C₂²	—	2	2	no	—
1369	C₂²	—	2	2	no	—
1370	C₂²	—	4	1	no	—
1371	C₂²	—	4	1	no	—
1372	C₂²	—	4	1	no	—
1373	C₂²	—	4	1	no	—
1374	C₂²	—	4	1	no	—
1375	C₂²	—	4	1	no	—
1376	C₂²	—	4	1	no	—
1377	C₂²	—	4	1	no	—
1378	C₂²	—	4	1	no	—
1379	C₂²	—	4	1	no	—
1380	C₂²	—	4	1	no	—
1381	C₂²	—	4	1	no	—
1382	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
1383	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1384	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1385	C₂²	C₃₁×#585	1	1	yes	characteristic
1386	C₂²	C₃₁×#585	1	1	yes	characteristic
1387	C₂²	C₃₁×#585	1	1	yes	characteristic
1388	C₂²	C₃₁×#585	1	1	yes	characteristic
1389	C₄	—	2	2	no	—
1390	C₄	—	2	2	no	—
1391	C₄	—	2	2	no	—
1392	C₄	—	2	2	no	—
1393	C₄	—	2	2	no	—
1394	C₄	—	2	2	no	—
1395	C₄	—	2	2	no	—
1396	C₄	—	2	2	no	—
1397	C₄	—	2	2	no	—
1398	C₄	—	2	2	no	—
1399	C₄	—	2	2	no	—
1400	C₄	—	2	2	no	—
1401	C₄	—	2	2	no	—
1402	C₄	—	2	2	no	—
1403	C₄	—	4	1	no	—
1404	C₄	—	4	1	no	—
1405	C₄	—	4	1	no	—
1406	C₄	—	4	1	no	—
1407	C₄	—	4	1	no	—
1408	C₄	—	4	1	no	—
1409	C₄	—	4	1	no	—
1410	C₄	—	4	1	no	—
1411	C₄	—	4	1	no	—
1412	C₄	—	4	1	no	—
1413	C₄	—	4	1	no	—
1414	C₄	—	4	1	no	—
1415	C₄	—	4	1	no	—
1416	C₄	—	4	1	no	—
1417	C₂	—	4	2	no	—
1418	C₂	—	4	2	no	—
1419	C₂	—	4	2	no	—
1420	C₂	C₃₁×#3428	1	1	yes	characteristic
1421	C₂	C₄×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1422	C₂	C₄×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1423	C₂	C₃₁×#3533	1	1	yes	characteristic
1424	C₂	C₃₁×#3541	1	1	yes	characteristic
1425	C₂	C₃₁×#3557	1	1	yes	characteristic
1426	C₂	C₃₁×#3567	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#121	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₃₁×#2382	C₂	semidirect
3. C₃₁×#2378	C₂	semidirect
4. C₃₁×#2378	C₂	semidirect
5. C₃₁×#2376	C₂	semidirect
6. C₃₁×#2374	C₂	semidirect
7. C₃₁×#2373	C₂	semidirect
8. C₃₁×#2373	C₂	semidirect
9. C₃₁×#2371	C₂	semidirect
10. C₃₁×#2370	C₂	semidirect
11. C₃₁×#2370	C₂	semidirect
12. C₃₁×#2362	C₂	semidirect
13. C₃₁×#2360	C₂	semidirect
14. C₃₁×#2357	C₂	semidirect
15. C₃₁×#2352	C₂	semidirect
16. C₃₁×#2345	C₂	semidirect
17. C₃₁×#2344	C₂	semidirect
18. C₃₁×#2335	C₂	semidirect
19. C₃₁×#2335	C₂	semidirect
20. C₃₁×#2335	C₂	semidirect
21. C₃₁×#2335	C₂	semidirect
22. C₃₁×#2334	C₂	semidirect
23. C₃₁×#2334	C₂	semidirect
25. C₃₁×#2332	C₂	semidirect
27. C₃₁×#2322	C₂	semidirect
28. C₃₁×#2319	C₂	semidirect
29. C₄×C₃₁×C₂²⋊Q₈	C₂	semidirect
30. C₄×C₃₁×#123	C₂	semidirect
31. C₃₁×#2290	C₂	semidirect
32. C₃₁×#539	C₄	semidirect
201. C₃₁×#126	C₂×C₄	semidirect
202. C₃₁×#126	C₂×C₄	semidirect
203. C₃₁×#125	C₂×C₄	semidirect
204. C₃₁×#125	C₂×C₄	semidirect
207. C₃₁×#123	C₂×C₄	semidirect
208. C₃₁×#123	C₂×C₄	semidirect
209. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
210. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
211. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
215. C₄×D₄×C₃₁	C₂×C₄	semidirect
216. C₄×D₄×C₃₁	C₂×C₄	semidirect
220. C₂×C₄⋊C₄×C₃₁	C₂×C₄	semidirect
528. #34449	C₃₁	direct (N × H)
649. #2382	C₂×C₃₁	semidirect
650. #2378	C₂×C₃₁	semidirect
651. #2378	C₂×C₃₁	semidirect
652. #2376	C₂×C₃₁	semidirect
653. #2374	C₂×C₃₁	semidirect
654. #2373	C₂×C₃₁	semidirect
655. #2373	C₂×C₃₁	semidirect
656. #2371	C₂×C₃₁	semidirect
657. #2370	C₂×C₃₁	semidirect
658. #2370	C₂×C₃₁	semidirect
659. #2362	C₂×C₃₁	semidirect
660. #2360	C₂×C₃₁	semidirect
661. #2357	C₂×C₃₁	semidirect
662. #2352	C₂×C₃₁	semidirect
663. #2345	C₂×C₃₁	semidirect
664. #2344	C₂×C₃₁	semidirect
665. #2335	C₂×C₃₁	semidirect
666. #2335	C₂×C₃₁	semidirect
667. #2335	C₂×C₃₁	semidirect
668. #2335	C₂×C₃₁	semidirect
669. #2334	C₂×C₃₁	semidirect
670. #2334	C₂×C₃₁	semidirect
672. #2332	C₂×C₃₁	semidirect
674. #2322	C₂×C₃₁	semidirect
675. #2319	C₂×C₃₁	semidirect
676. C₄×C₂²⋊Q₈	C₂×C₃₁	semidirect
677. C₄×#123	C₂×C₃₁	semidirect
678. #2290	C₂×C₃₁	semidirect
735. #539	C₄×C₃₁	semidirect
914. #126	C₂×C₄×C₃₁	semidirect
915. #126	C₂×C₄×C₃₁	semidirect
916. #125	C₂×C₄×C₃₁	semidirect
917. #125	C₂×C₄×C₃₁	semidirect
920. #123	C₂×C₄×C₃₁	semidirect
921. #123	C₂×C₄×C₃₁	semidirect
922. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
923. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
924. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
928. C₄×D₄	C₂×C₄×C₃₁	semidirect
929. C₄×D₄	C₂×C₄×C₃₁	semidirect
933. C₂×C₄⋊C₄	C₂×C₄×C₃₁	semidirect
1077. C₃₁	#34449	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃₁×#539	2
C₃₁×#2382	2
C₃₁×#2378	2
C₃₁×#2376	2
C₃₁×#2374	2
C₃₁×#2373	2
C₃₁×#2371	2
C₃₁×#2370	2
C₃₁×#2362	2
C₃₁×#2360	2
C₃₁×#2357	2
C₃₁×#2352	2
C₃₁×#2345	2
C₃₁×#2344	2
C₃₁×#2335	2
C₃₁×#2334	2
C₃₁×#2333	2
C₃₁×#2332	2
C₃₁×#2324	2
C₃₁×#2322	2
C₃₁×#2319	2
C₄×C₃₁×C₂²⋊Q₈	2
C₄×C₃₁×#123	2
C₃₁×#2290	2
#34449	31

Subgroups — C31×#34449 #21491208

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34449 #21491208